Timothy Murphy, L3 Applied Defense Solutions; Marcus Holzinger, University of Colorado Boulder
Keywords: Telescope, astrometry, photometry, exposure time, optimization
Abstract:
This work proposes a methodology for optimally selecting telescope mount and camera parameters when taking data for space situational awareness applications with various objectives. This work is formulated as a optimal design problem, treating the tasking parameters as design variables, the information content of the images as objectives, and the physical limitations of the telescope as constraints. The design variables are primarily the beginning and end times of each exposure, the slew rate of the telescope, and the gain. The primary objectives examined in this work are maximizing information of object location and speed in an image, and maximizing information on object brightness over time. Constraints include pixel saturation, star field clutter, and end constraints on timing.
The exposure time is formulated as a variable length vector, which takes into account the variable number of exposures which can be taken over a set campaign length. The objectives are formulated using Fisher information analysis on a maximum likelihood estimator. Each objective is derived for both stationary and streaking objects. The gradient with respect to exposure times is developed for each objective. For object speed in image, an novel formulation of velocity astrometry is presented. The astrometry results show a balance between long exposure to maximize SNR and a large time differential between images with which to estimate velocity. For photometry, aliasing error from photon flux variations over a particular exposure is incorporated as a source of extra noise. Photometry objective is shown to balance long exposures to minimize noise and short exposures to minimize aliasing. The cost function and gradients are all analytically derived and can therefore be efficiently calculated.
The final problem is a multi-objective optimization problem with a series of constraints and a variable length vector in the form of the exposure times. In simulation, each objective is explored individually. The photometry in particular is explored under both a low-amplitude variable signal and a high-amplitude which gives different results. The combined problem of photometry and astrometry is explored with a Pareto surface analysis. Particular solutions are pulled off the Pareto surface and observed more closely.
The resulting campaigns represent a shift from current state-of-the-art. Results found through optimization vary the exposure time as the data collection progresses.
Date of Conference: September 11-14, 2018
Track: Poster